A Nice Algebra Problem | Math Olympiad

A Nice Algebra Problem | Math Olympiad
Welcome to another exciting Math Olympiad challenge! In this video, we evaluate an intriguing algebraic expression that will test your simplification skills. Whether you're a math enthusiast or preparing for a competition, this problem is perfect for sharpening your algebra abilities.
Join us as we break down the steps and explore different strategies to simplify this interesting expression. Don't forget to pause the video and try it yourself before watching the solution. Let's see if you can crack it!
If you enjoy this type of content, make sure to like, comment, and subscribe for more math challenges and problem-solving tips. Happy simplifying!
🔢 What You'll Learn:
Key strategies for simplifying complex expressions
Tips and tricks to approach difficult simplification problems
Step-by-step walkthrough of the solution
🧠 Challenge Yourself:
Pause the video, try to solve the problem on your own, and then watch as we break down the solution. Share your approach and answers in the comments below!
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4. Join us and enhance your problem-solving skills. Can you master this simplification problem?
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Thanks for Watching !

[@user-kp2rd5qv8g]

We see that x+1/x = 3 and the expression we have to evaluate simplifies to f(x) =[x^10+1/x^10]/[x^9+1/x^9]. The numerator is 123^2-2 = 15127 and the denominator is 5778. So, the required expression is 15127/5778.

[@tunneloflight]

It is amazing how close this is to phi plus 1, yet not equal to it.

[@johnstanley5692]

A quick approximation? since X^5+1/X^5 = 123 => X^5 ~ (123-1/123) => X = (X^5)^(1/5) ~ 2.618.
for high powers ignore (1/x^n) terms : problem approximates to (X^11-X^9)/(X^10-X^8) = X =2.618. ( note 15127/5778 ~ 2.6180)